Improved and Generalized Criteria for the Instantaneous Regime for Multiple Parallel Gas-Liquid Reactions

Abstract

The classic criteria to determine if a second-order irreversible gas-liquid reaction (AG + BL → CL) proceeds in the instantaneous regime are based on the Hatta number, HaA, and the infinite enhancement factor, EA,inf, i.e., HaA > 2 and HaA ≫ EA,inf − 1. There is no consensus, with respect to the latter threshold value and this work shows that it highly depends on the considered reactant concentrations and rate coefficients. Moreover, these criteria are necessary but not sufficient in case the infinite enhancement factor is below 2. Generalizing the original derivation yields an extended expression, which is condensed into a new dimensionless number, φA,inf, and allows to rewrite the second criterion as φA,inf ≥ 15, where φA,inf=(!&’,#!)* − EA,inf. Next, it is demonstrated that a breakthrough of the gas-phase reactant into the bulk-liquid is readily observed at high interface concentrations of the gas-phase reactant with respect to the bulk concentration of the liquid-phase reactant, even though the classic criteria have been met. Such a situation is quite common in the chemical industry, e.g., in case of selective reactive removal of an impurity (BL) from a process stream containing a valuable product by a soluble gaseous component (AG). The root cause of this deviating behavior results from the position of the reaction plane and an additional criterion, φA,inf ≥ 15, is needed to resolve this. As such, the set of improved criteria are necessary and sufficient to describe the instantaneous regime for any position of the reaction plane. To conclude, a methodology is presented to apply the modified criteria to multiple parallel reactions, and the validity of these improved and generalized criteria is numerically demonstrated.

Keywords: Gas-Liquid mass transfer, instantaneous reaction, enhancement factor, Hatta number